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Unformatted text preview: d make use of all available edges.” 134 16 Energy and power 16.1 Power ﬂow optimization with ‘N − 1’ reliability constraint. We model a network of power lines as a
graph with n nodes and m edges. The power ﬂow along line j is denoted pj , which can be positive,
which means power ﬂows along the line in the direction of the edge, or negative, which means power
ﬂows along the line in the direction opposite the edge. (In other words, edge orientation is only
used to determine the direction in which power ﬂow is considered positive.) Each edge can support
power ﬂow in either direction, up to a given maximum capacity Pjmax , i.e., we have |pj | ≤ Pjmax .
Generators are attached to the ﬁrst k nodes. Generator i provides power gi to the network. These
must satisfy 0 ≤ gi ≤ Gmax , where Gmax is a given maximum power available from generator i.
The power generation costs are ci > 0, which are given; the total cost of power generation is cT g .
Electrical loads are connected to the nodes k + 1, . ....
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- Fall '13
- The Aeneid